Digital Fourier analysis: advanced techniques

摘要

If there was ever a "gift that keeps on giving" to the most esoteric of mathematico-physical theories or to the most pragmatic of engineering practice, it is Fourier analysis. (On my bucket list is someday to discover, in principle from Georg Cantor's original papers, exactly how Cantor's seminal and arguably still-controversial set theory emerged from his study of 19th-century Fourier analysis.) Just as the principle of least action retains a mystery (that is not born of mysticism) regarding its effectiveness in both classical and quantum physics, so Fourier analysis realizes to an astounding degree the assertion, variously attributed to James Clerk Maxwell or David Hilbert, that "there is nothing more practical than a good theory."